1. Field of the Invention
This invention relates to the field of electrochemistry, and more particularly, it relates to the coulometric analysis of specific ions in an electrolytic solution.
2. Description of the Prior Art
Coulometric analysis for specific ions in an electrolytic solution is a well known and established technique in the field of electrochemistry. The development of automatic functioning coulometric titrators for carrying out these analyses has produced many devices of which examples may be found in U.S. Pat. Nos. 3,275,533, 3,398,064, 3,441,490 and 3,647,668. Known automatic titration devices in the electrochemical field for conducting coulometric analysis depend upon a feedback loop which supplies an error signal establishing some fixed relationship between the addition of the reactive ion and a reference point at which the titration of the specific ion sought is believed to have been completed. Obviously, the feedback loop principle is a time domain function and suffers from compound errors. The electrodes employed in conducting the electrochemical analysis have an appreciable capacitance characteristic. Also, an appreciable time delay is caused by the diffusion of ions in the cell and principally the reactive ions introduced into the solution by the coulometric flow of current into the cell. Thus, the time delay problems make inaccurate and difficult-to-produce results in the coulometric titration of specific ions in an aqueous solution. The operator or an automatic feature must terminate with high accuracy and precision in electrochemical analysis the introduction of the reactive ion so that the ions may properly diffuse and the cell "coast" to what is believed to be the actual endpoint. The time delay problem varies with ion concentration and kind which also compounds the problem. The actual endpoint also changes not only with different types of ion but with different solvent composition.
It will be apparent that the coulometric titration employs sensors for the detection of the specific ion whose output, according to the Nernst equation, is a voltage proportional to the logarithm of the specific ion concentration. Thus, the most important component of the coulometric titration system is the sensor for the specific ion. The sensor has to indicate when a sufficient amount of the reactive ion has been added to completely convert this specific ion being analyzed for into a product effectively combining the specific and reactive ions into an insoluble or otherwise non-reactive salt. The sensor must be sensitive only to the specific ion being analyzed, and also, the reactive ion must combine only with the specific ion subject to analysis. Further, there must be a definite relationship in the chemical reaction between the specific and reactive ions and freedom from any interferences by extraneous ions with the desired reaction.
Obviously, automatic functioning coulometric titrators usually depend on electrochemical sensors whose voltage output is proportional to the logarithm of the concentration of the specific ion subject to analysis. This relationship is well known as the Nernst equation. This equation is a proper definition for the steady state of a solution or one where the ion concentrations are changing at a very slow rate. Mathematically, the equation defines that a certain percentage change in specific ion concentration will cause an incremental change in sensor output voltage that is the same independent of the actual magnitude of the specific ion concentration. Therefore, in the automatic coulometric titrator, the electrochemical sensor can be incorporated in its function as a percentage change indicator relative to the specific ion concentration.
As will be apparent, the addition of the reactive ion to the test solution at a constant rate produces ambiguities in the sensor's logarithmic voltage output. More particularly, the specific ion sensor changes voltage at the most rapid rate when the specific ion concentration is at equivalence since the largest percent change in specific ion concentration occurs at this point of the analysis. Therefore, the maximum sensor voltage change and the maximum rate of percentage change of specific ion concentration is known as the inflection point of the electrochemical analysis. High accuracy can be obtained with a constant rate of reactive ion addition only if the electrochemical analysis is done at very low rates of reactive ion addition so that the dynamic problems relating to the phenomena do not cause large analysis errors, but the time of analysis is very long.
The above dynamic electrochemical analysis problems can be very severe when the specific ion sensor suffers from capacitive or any energy storage characteristics in the electrolytic solution. The capacitance function in a dynamic electrochemical analysis requires that the specific ions must either enter or leave the region of the sensor for the voltage output to change. In the optimum form of the coulometric titrator, the transfer of the specific ions and voltage output change are usually independent of the specific ion concentration in the solution and dependent only on the physical construction of the sensor. However, where the capacitance function is encountered, these relationships are no longer valid and appreciable time delay errors arise in this electrochemical analysis.
Unfortunately, the capacitive function about the sensor electrode produces a time delay that becomes proportionally larger as the concentration of the specific ions approaches equivalence. At equivalence concentration levels of the specific ions, the time delay problem causes the most error in the electrochemical analysis since the sensor fails to indicate by output voltage the endpoint until some extended period of time after the actual endpoint has been passed by the continued addition of the reactive ion.
In an application of Homer M. Wilson, application Ser. No. 643,064, filed Dec. 22, 1975, there is disclosed a coulometric titrator arranged to avoid the problems of the time delay error and capacitance function about the sensor electrode. In said coulometric titrator, the novel improvement in electrochemical analysis is achieved by scaler (non-time domain) circuitry which reduces the rate of reactive ion addition logarithmically throughout the analysis. In the preferred embodiment of said coulometric titrator, the addition of the reactive ion is made proportional to the ratio of the anti-logarithm of the specific ion sensor's voltage output and a certain rate controlling reference voltage. In said coulometric titrator, the factor change in the specific ion concentration remains constant and yields a linear rate of sensor voltage change with time. As a result, any dynamic time delay arising from the characteristics of the sensor in detection of the specific ion concentration will have a rate controlling influence and not an endpoint controlling influence. The linear rate of change of sensor output voltage with time is set by the rate controlling reference voltage. Thus, said Wilson coulometric titrator provides not only high speed titrations of great accuracy, but it employs the linear sensor output voltage change to indicate to the operator that the choice of electrochemical analysis parameters is correct.
Since said Wilson titrator has been designed to provide reactive ion proportional to the amount of specific ion left to titrate and has no capability for any other reactive ion demand, the stopping point occurs when some unexpected reactive ion demand becomes the predominant user of the available reactive ion. Said unexpected reactive ion demand of said Wilson titrator is usually the demand for storage of the reactive ion in solution as free ion. Because the characteristics of ions in solution determine the stopping point, any zero shift in sensor voltage does not change the stopping point, but only changes the rate of speed that the stopping point is approaching. The Wilson titrator thus permits accurate operation and accurate answers even though the sensor voltage signal has unexpectedly or even intentionally been shifted by some d.c. amount. Titrators other than the Wilson titrator at the time of the Wilson invention were very dependent on the use of a stable sensor voltage signal and any unexpected shift in sensor voltage signal was such as would cause considerable error in the answer without the operator being conscious of the problem.
Said Wilson invention provided a coulometric titrator for determining the amount of a specific ion in a sample electrolytic solution by the controlled addition of a reactive ion. Said Wilson titrator includes a reference electrode providing a first signal voltage and a specific ion sensing electrode providing a second signal voltage representing the logarithm of the concentration of the specific ion in the same solution in which these electrodes are immersed. Therein, a differential input amplifier receives these first and second signal voltages as its input and provides in its output an error signal voltage representing the difference between the first and second signal voltages; a reference means provides reference voltage for the specific ion in the solution indicative of a particular rate of change of the second signal voltage while the rate of change of the second signal voltage is constant. In addition, in said Wilson titrator, comparator means receive the error signal and the referenced voltage as inputs and has an output of a sensor signal voltage representing the difference between the error signal and reference voltage, and the sensor signal voltage is applied to an antilogarithm converter means which produces an output signal that is proportional to the antilogarithm of the sensor signal voltage. Furthermore, in Wilson, reactive ion source means receive the output signal and are associated with a current source providing a unidirectional current flow between a cathode and an anode immersed in the same solution (one being inert and the other being the reactive ion means) such that the quantum rate of the reactive ion introduced into the sample solution is proportional to the control signal. As a result, in the Wilson titrator, the second signal voltage changes at a constant rate with time and the reactive ion addition changes in a logarithmically decreasing amount with time in the same solution.
In other embodiments of said Wilson invention, a differentiator means may be employed to receive the error signal voltage and to provide a readout representing the change in the error signal voltage with time, and, when the proper rate controlling reference voltage has been selected, this readout is a steady state signal of between 10 and 60 millivolts per minute. Also, in the Wilson invention, a coulometric means may be employed to monitor the coulombs supplied to the reactive ions source means.
In said Wilson titrator, the current at the generating electrodes is controlled by the sensing electrodes and is given by the relationship i=i.sub.o antilog [-D(E-E.sub.o)], wherein i.sub.o is the referencing current, E-E.sub.o the sensor signal voltage and the constant D controls the slope or rate of application of generating current; a value for D which is suitable for a one electron reaction (n=1) will result in an impractically low titration rate where two (n=2) and three (n=3) electron reactions are involved.
Moreover, in the Wilson titrator, only systems in which the error signal voltage E increases in a positive direction are capable of being titrated.
An object of the present invention is to provide an improvement over the Wilson titrator which enables it to carry out titrations at a practical rate regardless of the number of electrons (n) involved in the reaction.
An additional object is to provide an improvement in said Wilson titrator which enables it to be used in systems in which the signal voltage increases in a negative manner as well as those in which it increases in a positive manner.
Other objects of this invention will be apparent hereinafter.